Problem: This is the easy version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.

Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version all prices are different.

An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.

You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.

The second line contains n different integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.

Output

In the first line print the maximum number of ice spheres that Sage can buy.

In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.

Example

Input


5
1 2 3 4 5


Output


2
3 1 4 2 5 

Note

In the example it's not possible to place ice spheres in any order so that Sage would buy 3 of them. If the ice spheres are placed like this (3, 1, 4, 2, 5), then Sage will buy two spheres: one for 1 and one for 2, because they are cheap.

Solution (in PYTHON):

Solution:
# encoding:utf-8

'''
今天是鸭鸭的生日，她要出门去买娃娃作为礼物，有n个娃娃排成一排，编号从1到n，每个娃娃都有个价格（正整数），有些娃娃的价格会相等。

一个娃娃的价格被定义为便宜，如果它比它左右紧挨着的娃娃价格都低。最左边和最右边的娃娃都无法被定义为便宜，鸭鸭想买下所有便宜的娃娃。

为了让鸭鸭有更大的惊喜，你要在她到来之前将娃娃摆好，想办法能够让便宜的娃娃尽可能的多，希望你能够找到这种最佳的摆法。
'''

def process(sorted_array):
    right_start_index = len(sorted_array) // 2
    i = 0
    j = 0
    res_num = 0
    res_list = []
    for j in range(right_start_index, len(sorted_array)-1):
        if sorted_array[j] > sorted_array[i]:
            res_num += 1
            res_list.extend([sorted_array[j], sorted_array[i]])
            i += 1
        else:
            res_list.append(sorted_array[j])
    res_list.append(sorted_array[j+1])
    for k in range(i, right_start_index):
        res_list.append(sorted_array[k])
    return res_num, res_list

def main():
    len_ = raw_input()
    input_array = map(int, raw_input().split())
    if int(len_) <= 2:
        print 0
        print ' '.join(map(str, input_array))
        return
    # print len_, input_array
    input_array.sort()
    res_num, res_list = process(input_array)
    print res_num
    print ' '.join(map(str, res_list))

if __name__ == '__main__':
    main()